The general definition.

Definition 4.1.1   Let $ x_0 \in \overline{\mathbb{R}}$ and $ l \in \overline{\mathbb{R}}$ . Let $ f$ be a function defined on a (pointed) neighborhood $ D$ of $ x_0$ . The element $ l$ is the limit of $ f$ when $ x$ tends to $ x_0$ if for every neighborhood $ V$ of $ l$ there exists a neighborhood $ U$ of $ x_0$ such that $ f(U) \subset V$ .

Notation: $ \underset{x \rightarrow x_0}{\lim} f(x) = l$ .

This general definition can be dispatched into several particular ones:



Subsections

Noah Dana-Picard 2007-12-28